# Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.

Let the two concentric circles be centred at point O. And let PQ be the chord of the larger circle which touches the smaller circle at point A. Therefore, PQ is tangent to the smaller circle.

OA PQ (As OA is the radius of the circle)

Applying Pythagoras theorem in ΔOAP, we obtain

OA2 + AP2 = OP2

32 + AP2 = 52

9 + AP2 = 25

AP2 = 16

AP = 4

In ΔOPQ,

Since OA PQ,

AP = AQ (Perpendicular from the centre of the circle bisects the chord)

PQ = 2AP = 2 × 4 = 8

Therefore, the length of the chord of the larger circle is 8 cm.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Quiz | Imp. Qs. on Circles37 mins
Quiz | Testing Your Knowledge on Circles32 mins
Short Cut Trick to Find Area of Triangle43 mins
Quiz | Areas Related to Circles43 mins
RD Sharma | Area of Sector and Segments25 mins
Quiz | Area Related with Circles47 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses